使用 Newell 方法在 Python 中计算表面法线 [英] Calculating surface normal in Python using Newell's Method

问题描述

我正在尝试基于来自 这里.

I'm trying to implement Newell's Method to calculate the surface normal vector in Python, based on the following pseudocode from here.

Begin Function CalculateSurfaceNormal (Input Polygon) Returns Vector

   Set Vertex Normal to (0, 0, 0)

   Begin Cycle for Index in [0, Polygon.vertexNumber)

      Set Vertex Current to Polygon.verts[Index]
      Set Vertex Next    to Polygon.verts[(Index plus 1) mod Polygon.vertexNumber]

      Set Normal.x to Sum of Normal.x and (multiply (Current.y minus Next.y) by (Current.z plus Next.z))
      Set Normal.y to Sum of Normal.y and (multiply (Current.z minus Next.z) by (Current.x plus Next.x))
      Set Normal.z to Sum of Normal.z and (multiply (Current.x minus Next.x) by (Current.y plus Next.y))

   End Cycle

   Returning Normalize(Normal)

End Function

这是我的代码:

Point3D = collections.namedtuple('Point3D', 'x y z')

def surface_normal(poly):
    n = [0.0, 0.0, 0.0]

    for i, v_curr in enumerate(poly):
        v_next = poly[(i+1) % len(poly)]
        n[0] += (v_curr.y - v_next.y) * (v_curr.z - v_next.z)
        n[1] += (v_curr.z - v_next.z) * (v_curr.x - v_next.x)
        n[2] += (v_curr.x - v_next.x) * (v_curr.y - v_next.y)

    normalised = [i/sum(n) for i in n]

    return normalised

def test_surface_normal():
    poly = [Point3D(0.0, 0.0, 0.0),
            Point3D(0.0, 1.0, 0.0),
            Point3D(1.0, 1.0, 0.0),
            Point3D(1.0, 0.0, 0.0)]

    assert surface_normal(poly) == [0.0, 0.0, 1.0]

这在规范化步骤失败，因为此时 n 是 [0.0, 0.0, 0.0].如果我理解正确，它应该是 [0.0, 0.0, 1.0] (确认 由 Wolfram Alpha).

This fails at the normalisation step since the n at that point is [0.0, 0.0, 0.0]. If I'm understanding correctly, it should be [0.0, 0.0, 1.0] (confirmed by Wolfram Alpha).

我在这里做错了什么?有没有更好的方法来计算 python 中的表面法线?我的多边形将始终是平面的，因此如果有另一种方式，纽厄尔方法并不是绝对必要的.

What am I doing wrong here? And is there a better way of calculating surface normals in python? My polygons will always be planar so Newell's Method isn't absolutely necessary if there's another way.

推荐答案

好吧，这个问题其实很蠢.

Ok, the problem was actually a stupid one.

像这样的行:

n[0] += (v_curr.y - v_next.y) * (v_curr.z - v_next.z)

应该是:

n[0] += (v_curr.y - v_next.y) * (v_curr.z + v_next.z) 

第二组括号中的值应该相加，而不是相减.

The values in the second set of brackets should be added, not subtracted.

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